Spectral residual tests

The spectral residual plot in Fig. 15 was chosen to illustrate an obvious outlier (sample No. 45). It is necessary to use the F test method to determine that the samples are indeed outliers in the same maimer that is used for concentration outliers. For spectral residuals, the F ratio is calculated as... 

By calculating the sum of the squares of the spectral residuals across all the wavelengths, an additional representative value can be generated for each spectrum. The spectral residual is effectively a measure of the amount of each spectrum left over in the secondary or noise vectors. This value is the basis of another type of discrimination method known as SIMCA (Refs. 13, 36). This is similar to performing an F test on the spectral residual to determine outliers in a training set (see Outlier Sample Detection in Chapter 4). In fact, one group combined the PCA-Mahalanobis distance method with SIMCA to provide a biparametric method of discriminant analysis (Ref. 41). In this method, both the Mahalanobis distance and the SIMCA test on the spectral residual had to pass in order for a sample to be classified as a match. 

Equation (4.20) was proposed by Hoskuldsson [65] many years ago and has been adopted by the American Society for Testing and Materials (ASTM) [59]. It generalises the univariate expression to the multivariate context and concisely describes the error propagated from three uncertainty sources to the standard error of the predicted concentration calibration concentration errors, errors in calibration instrumental signals and errors in test sample signals. Equations (4.19) and (4.20) assume that calibrations standards are representative of the test or future samples. However, if the test or future (real) sample presents uncalibrated components or spectral artefacts, the residuals will be abnormally large. In this case, the sample should be classified as an outlier and the analyte concentration cannot be predicted by the current model. This constitutes the basis of the excellent outlier detection capabilities of first-order multivariate methodologies. 

A fundamental problem of reaction simulation is the choice of an appropriate reaction model. No standard procedure for this problem can be found in the literature. It is essential, therefore, that model-based measurements of reaction data support the task of model selection. Generally, the residuals in the comparison of the data from the modelled reaction with the experimental measurements are taken as an indication of the quality of the reaction model. However, the robustness of the model fit generally decreases with increasing number of reaction parameters (such as rate constants, activation energies, reaction enthalpies or spectral absorbances) that have to be determined. In this example, we demonstrate how different reaction models can be postulated and then tested on the basis of calorimetric and IR-ATR measurements. 

A reduction of the interferences resulting both from spectral overlap and ionization can be realized in a number of cases by removal of acids and matrix residuals, as shown by on-line removal of these species by separations on solid phases, which has now been tested in the case of exchanges made at modified nebulizer surfaces [517]. 

Nuclear Magnetic Resonance Procedure—Small samples of the original oils and the volatile materials and residues obtained during the special Noack tests were analyzed by P NMR at Washington University (St. Louis, MO). The spectra were obtained either on a 500 MHz Varian NMR equipped with a 10 mm probe or on a 600 MHz Varian NMR equipped with a 5 mm probe. Samples were diluted with 10-15 % chloroform-d (CDC13), which also served as an internal reference for establishing spectral positions. Average data accumulation time for these spectra was one hour. As mentioned, a conjoined paper [24] covers this aspect of the study. 

To test the dominance of electrostatic effects in the mineralization model, a mutant of CCMV was constructed (subE) in which all the basic residues on the N-terminus of the coat protein were substituted for glutamic acid (E), thus dramatically altering the electrostatic character of the interior of the assembled protein cage." This mutant was able to catalyze the oxidative hydrolysis of Fe(II) to form an iron oxide nanoparticle encapsulated within the protein cage of the modified virus. High-rcsolution spectral imaging allowed the elemental composition of a protein-mineral composite material to be resolved (1 nm spatial resolution, Fig. 3). This clearly showed that the mineral nanoparticle was completely encapsulated within the protein cage structure. This mutant is able to bind Fe(lT), facilitate its autoxidation... 

Conditions 1 and 3 require that the underlying physical phenomenon responsible for generating the mean photon rate stays constant over the period of time in which Eq. (4.44) is tested or employed. TTiis means that the half-life of the radioisotope must be long compared to the measurement time in the case of radioisotope excitation, and the x-ray tube spectral content and intensity must be constant over the measurement time in the case of x-ray tube excitation. X-ray photons from radioisotopes with very short half-lives, from pulsed x-ray tubes, or from x-ray tubes exhibiting significant residual line frequency ripple, will not be distributed according to Eq. (4.44). 

The light beam emitted by the incandescent lamp or a metal vapour lamp (e.g. Hg or Cd vapour lamp) is "sorted by the spectral filter in such a way that it is virtually monochromatic. As such it passes through the cuvette containing the solution of the substance to be determined (after exchanging the sample cuvette for a blank-test cuvette containing pure solvent). After leaving the cuvette the residual light intensity I of the beam is converted to an electric current in the photoelectric cell... 

The Mahalanobis distance tests whether or not an unknown fits within the limits of any known groups. The residual represents the spectral information that remains after the principal components... 

Search systems are powerful tools, but as for most algorithms described in this chapter, care must be taken when they are used. The unknown and the hbrary spectra must both obey Beer s law. Care must be taken that the wavenumber calibration of an instrument is correct as wavenumber shifts may occur between the unknown and the hbrary spectra. The algorithms compensate for spectral shifts to some degree, but they cannot compensate for large shifts. In addition, the spec-troscopist must remember two important caveats (1) a hbrary search cannot identify an unknown unless the unknown is in the hbrary and (2) a high value of the hit quality index is not necessarily an indication of a correct match. The judicious spec-troscopist will visually compare the spectra of the unknown to the best matches to determine if they are indeed identical. In fact, the best test is to perform a spectral subtraction between the unknown and the hbrary match to see if there is a nonzero residual. If the two spectra are not identical, a nonzero subtraction will result. Finally, it should be recognized that spectral similarity does not indicate structural similarity. Certainly, some of the functional groups in structurally similar molecules will be the same, but the overall structure of an unknown and the best matches that result from a search may be quite different. 

An essential element in this program is the preparation of pure protein derivatives site specifically labeled by a donor and acceptor and their characterization. Several methods were developed for speci-fic labeling of globular proteins and applied in the preparation of fluorescent derivatives of bovine pancreatic trypsin inhibitor (BPTI) and ribonuclease (RNase). Methoxy-naphthyl derivatives are used as donor chromophores, in particular 2-methoxy-1-naphthyl-methylenyl (MNA) and 2-naphthoxy-acetyl (NAA) were used as donor chromophores (Fig. 3). These two probes are characterized by spectral characteristics suitable for measurements by the present methods (Fig. 4). In particular,they both show monoexponential decay when attached to the protein in the absence of an acceptor under all experimental conditions tested so far. This is a key element in the analysis of fluorescence decay curves of donor-acceptor labeled derivatives, in which all deviations from monoexponential decay are interpreted as distributions of distance. 7-dimethylamino-coumarine-4-acetyl (DA-coum) or 2,4-dinitrophenyl residues were used as acceptors. 

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